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xii | |
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xiv | |
Acknowledgements |
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xvi | |
Introduction |
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1 | (20) |
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Set-theoretic approaches in the social sciences |
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1 | (7) |
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Qualitative Comparative Analysis as a set-theoretic approach and technique |
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8 | (5) |
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13 | (3) |
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16 | (3) |
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19 | (2) |
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Part I Set-theoretic methods: the basics |
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21 | (96) |
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1 Sets, set membership, and calibration |
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23 | (19) |
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24 | (8) |
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24 | (1) |
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1.1.2 The pros and cons of crisp sets |
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24 | (3) |
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1.1.3 Properties of fuzzy sets |
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27 | (3) |
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1.1.4 What fuzzy sets are not |
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30 | (2) |
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1.2 The calibration of set membership |
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32 | (10) |
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1.2.1 Principles of calibration |
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32 | (1) |
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1.2.2 The use of quantitative scales for calibration |
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33 | (2) |
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1.2.3 The "direct" and "indirect" methods of calibration |
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35 | (3) |
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1.2.4 Does the choice of calibration strategy matter much? |
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38 | (2) |
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1.2.5 Assessing calibration |
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40 | (2) |
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2 Notions and operations in set theory |
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42 | (14) |
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2.1 Conjunctions, Boolean and fuzzy multiplication, intersection, logical AND |
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42 | (3) |
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2.2 Disjunctions, Boolean and fuzzy addition, union, logical OR |
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45 | (2) |
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2.3 Negations, complements, logical NOT |
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47 | (1) |
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2.4 Operations on complex expressions |
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47 | (5) |
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2.4.1 Rules for combining logical operators |
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48 | (1) |
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2.4.2 Negation, intersection, and union of complex sets |
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49 | (2) |
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2.4.3 Calculating membership in complex sets |
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51 | (1) |
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2.5 Relations between sets |
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52 | (2) |
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2.6 Notational systems in set-theoretic methods |
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54 | (2) |
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56 | (35) |
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3.1 Sufficient conditions |
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57 | (12) |
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57 | (8) |
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65 | (4) |
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69 | (7) |
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69 | (6) |
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75 | (1) |
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3.3 Causal complexity in set-theoretic methods |
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76 | (15) |
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3.3.1 Defining causal complexity |
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78 | (1) |
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3.3.2 INUS and SUIN conditions |
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79 | (2) |
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3.3.3 The notion of asymmetry |
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81 | (2) |
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3.3.4 Set-theoretic methods and standard quantitative approaches |
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83 | (8) |
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91 | (26) |
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4.1 What is a truth table? |
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92 | (1) |
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4.2 How to get from a data matrix to a truth table |
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93 | (11) |
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93 | (3) |
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96 | (8) |
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4.3 Analyzing truth tables |
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104 | (13) |
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4.3.1 Matching similar conjunctions |
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105 | (3) |
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4.3.2 Logically redundant prime implicants |
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108 | (4) |
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4.3.3 Issues related to the analysis of the non-occurrence of the outcome |
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112 | (5) |
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Part II Neat formal logic meets noisy social science data |
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117 | (78) |
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119 | (32) |
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5.1 Defining and dealing with contradictory truth table rows |
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120 | (3) |
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5.2 Consistency of sufficient conditions |
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123 | (6) |
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5.3 Coverage of sufficient conditions |
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129 | (10) |
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5.4 Consistency of necessary conditions |
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139 | (5) |
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5.5 Coverage of necessary conditions |
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144 | (4) |
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5.6 Issues related to consistency and coverage |
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148 | (3) |
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6 Limited diversity and logical remainders |
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151 | (27) |
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6.1 Limited diversity in set-theoretic methods: how to see it when it is there |
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152 | (1) |
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6.2 Sources of limited diversity |
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153 | (4) |
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6.2.1 Arithmetic remainders |
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154 | (1) |
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6.2.2 Clustered remainders |
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154 | (1) |
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6.2.3 Impossible remainders |
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155 | (2) |
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6.3 What limited diversity is not |
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157 | (3) |
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6.4 The Standard Analysis procedure: identifying logical remainders for crafting plausible solution terms |
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160 | (18) |
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6.4.1 The dimension of set relations |
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161 | (4) |
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6.4.2 The dimension of complexity |
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165 | (2) |
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6.4.3 The dimension of types of counterfactuals |
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167 | (8) |
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6.4.4 The Standard Analysis procedure in a nutshell |
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175 | (3) |
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7 The Truth Table Algorithm |
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178 | (17) |
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7.1 From the data matrix to truth table |
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179 | (3) |
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7.2 Attributing an outcome value to each truth table row |
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182 | (4) |
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7.3 Logically minimizing the truth table |
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186 | (4) |
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7.4 Implications of the Truth Table Algorithm |
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190 | (5) |
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Part III Potential pitfalls and suggestions for solutions |
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195 | (56) |
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8 Potential pitfalls in the Standard Analysis procedure and suggestions for improvement |
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197 | (23) |
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8.1 Beyond the Standard Analysis: expanding the types of counterfactuals |
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198 | (2) |
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8.2 The Enhanced Standard Analysis: forms of untenable assumptions and how to avoid them |
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200 | (11) |
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8.2.1 Incoherent counterfactuals I: contradicting the statement of necessity |
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201 | (2) |
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8.2.2 Incoherent counterfactuals II: contradictory assumptions |
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203 | (3) |
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8.2.3 Implausible counterfactuals: contradicting common sense |
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206 | (3) |
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8.2.4 Putting the Enhanced Standard Analysis procedure into practice |
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209 | (2) |
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8.3 Theory-Guided Enhanced Standard Analysis: complementary strategies for dealing with logical remainders |
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211 | (6) |
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8.3.1 Choosing entire truth table rows as good counterfactuals |
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212 | (3) |
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8.3.2 Formulating conjunctural directional expectations |
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215 | (2) |
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8.4 Comparing the different strategies for the treatment of logical remainders |
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217 | (3) |
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9 Potential pitfalls in the analysis of necessity and sufficiency and suggestions for avoiding them |
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220 | (31) |
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9.1 Pitfalls in inferring necessity from sufficiency solution terms |
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221 | (11) |
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9.1.1 Hidden necessary conditions |
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221 | (6) |
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9.1.2 The appearance of false necessary conditions |
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227 | (5) |
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9.2 The analytic consequences of skewed set-membership scores |
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232 | (19) |
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9.2.1 The coverage of necessary conditions and the problem of trivialness |
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233 | (4) |
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9.2.2 The consistency of sufficient conditions and the problem of simultaneous subset relations |
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237 | (7) |
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9.2.3 A general treatment of skewed set membership in fuzzy-set analyses |
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244 | (7) |
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Part IV Variants of QCA as a technique meet QCA as an approach |
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251 | (71) |
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253 | (22) |
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10.1 The two-step approach |
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253 | (2) |
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255 | (8) |
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10.2.1 Principles of mvQCA: notation and logical minimization |
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256 | (2) |
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10.2.2 An assessment of mvQCA |
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258 | (5) |
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10.3 Set-theoretic methods and time |
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263 | (12) |
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10.3.1 Forms of causally relevant notions of time |
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264 | (1) |
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10.3.2 Informal ways of integrating notions of time into set-theoretic methods |
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265 | (1) |
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10.3.3 Sequence elaboration |
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266 | (3) |
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269 | (6) |
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11 Data analysis technique meets set-theoretic approach |
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275 | (38) |
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11.1 Recipe for a good QCA |
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275 | (9) |
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11.1.1 The appropriateness of set-theoretic methods |
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276 | (1) |
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11.1.2 The choice of the conditions and the outcome |
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276 | (1) |
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11.1.3 The choice of the QCA variant |
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277 | (1) |
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11.1.4 Calibration of set-membership scores |
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277 | (1) |
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11.1.5 Analysis of necessary conditions |
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278 | (1) |
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11.1.6 Analysis of sufficient conditions |
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278 | (2) |
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11.1.7 Presentation of results |
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280 | (1) |
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11.1.8 Interpretation of results |
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280 | (1) |
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11.1.9 Reiteration of the research cycle |
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281 | (1) |
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11.1.10 The use of software |
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282 | (2) |
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11.2 Robustness and uncertainty in QCA |
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284 | (11) |
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11.2.1 How do we see robustness in set-theoretic methods when it is there? |
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285 | (2) |
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11.2.2 The effects of changing calibration |
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287 | (4) |
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11.2.3 The effects of changing consistency levels |
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291 | (2) |
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11.2.4 The effect of dropping or adding cases |
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293 | (2) |
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11.3 The evaluation of theories in set-theoretic methods |
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295 | (10) |
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11.3.1 Why standard hypothesis testing does not fit into set-theoretic methods |
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296 | (1) |
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11.3.2 The basics of theory evaluation in set-theoretic methods |
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297 | (3) |
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11.3.3 Extending theory evaluation by integrating consistency and coverage |
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300 | (4) |
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11.3.4 Summarizing set-theoretic theory evaluation |
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304 | (1) |
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11.4 Set-theoretic methods and case selection |
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305 | (8) |
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11.4.1 Types of cases after a QCA |
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306 | (2) |
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11.4.2 Forms and aims of (comparative) within-case studies after a QCA |
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308 | (2) |
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11.4.3 Post-QCA case selection principles |
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310 | (3) |
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12 Looking back, looking ahead |
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313 | (9) |
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12.1 Looking back: the main topics of this book |
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313 | (3) |
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12.2 Myths and misunderstandings |
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316 | (2) |
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12.3 Looking ahead: tasks and developments in the coming years |
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318 | (4) |
Glossary |
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322 | (14) |
Bibliography |
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336 | (10) |
Index |
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346 | |